What are Jacobi coordinates, and why are they useful?

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SUMMARY

Jacobi coordinates are essential for simplifying calculations in quantum chemistry, particularly when dealing with triatomic molecules. These coordinates utilize the center of mass of two bodies and are defined as R=(r1+r2+r3)/3, r=(r1-r2)/2, and rho=(2/3)[r3-(r1+r2)/2]. While the more common Jacobi coordinates introduce square roots for symmetry, they complicate practical applications. When working with bodies of unequal mass, mass considerations must be integrated into the calculations.

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What are "Jacobi coordinates," and why are they useful?

I am working on a quantum chemistry problem involving triatomic molecules. My advisor keeps talking about "Jacobi coordinates" and how they're a calculational convenience when it comes time to write out the Hamiltonian. Can someone describe them to me, and why they make life easier? I can't seem to find a good resource for this on the Web...
 
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Jacobi coordinates are coordinates for three bodies of equal mass, using the cm of two of them. The coordinates I like to use are
R=(r1+r2+r3)/3
r=(r1-r2)/2
rho=(2/3)[r3-(r1+r2)/2].
The more common Jacobi coordinates divide by square roots to make equations more symmetric, but they get more complicated in practice.
If one of the bodies has a different mass, then masses have to enter.
 

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